Two simultaneously-valid post-selection confidence intervals for network group densities are constructed, and the Talagrand-based one is shown sup-norm rate-optimal.
Proof.The inequalityE[||Z|| ∞→1]≤2E[||Z|| †] is Theorem 3 of Gittens and Tropp (2009)
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Post-Selection Inference for Network Structure
Two simultaneously-valid post-selection confidence intervals for network group densities are constructed, and the Talagrand-based one is shown sup-norm rate-optimal.